# Full text of "History Of The Theory Of Numbers - I"

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```486
SUBJECT INDEX
Primes 6w=*=l, 7 (see-difference, highest)
---------, asymptotic distribution of, 439, 449
---------, density of, 329, 416
-in arith. progression,
425
-, infinity of, 413
arith. progressions, 85,395, 415-20, 436
-, large,    352-4,    362,
365, 386, 388
~, law of apparition of,
396, 398, 406
- repeti-
tion of, 396-8 -------, miscellaneous results
on, 436-9 -------, number   of,   352-4,
429-35, 450
-------, product of, 126
ratic forms, 417
• poly-
nomials,   333,   414, "418,
420-1 --------, sum of two, 421-4,
435
Primes, tables of, 347, 381 --------, test for, 35, 276, 302,
305, 360-65, 370, 374, 376-
8, 380, 396-404, 426-8,445
---------, to base 2, 22, 353-4
Primitive divisor of an-bn, 388
--------X-root, 202
--------non-deficient number,
31
--------number, 327, 334
--------root, 63, 65, 72, 103,
117, 181-204, 222, 378-9
--------  --------1   imaginary,
235-252
136
Probability, 138, 302, 308, 328, 330, 333, 335, 407,438
Product of consecutive integers, 79, 263-4, 269, 331
-----------------differences, 269
------------------divisors, 58,
332
Pronic, 357
Quadratic forms, 109, 130, 158, 207, 210, 219, 276, 318, 330, 361-5, 369-70, 400, 415-8, 420-1
-------- residues-, 23, 25, 29,
65-8, 71, 76, 92, 109, 165,
- of unity, 133,
185, 189, 190, 196-8, 202, 210, 213-4, 218, 221, 231, 240,   245-6,   253-5,   275, 277,  360,  363,  365,  373, 382, 393, 395-6, 403 Quasi-Mersenne number, 390 Quotient (atf.™)— l)/m, 102, 105-112
--------- {(p-l)! + l}/p, 109,
112
Rank (see matrix)
Recurring series, 376-7, 393-411
------------------, algebraic theory of, 407
Reducible law of recurrence, 409-10
Redundantem, 3, 4
Remainders on dividing n by !,...,», 290, 313,327-31
Roots of unity, 133,136,183-4, 245, 250, 256, 419
Secondary number, 327
--------root, 191
Series of composition, 332
------------------Lame, 411
------------------Leonardo Pis-
ano, 393 Sieve   of   Eratosthenes,   8,
347-8, 353-6, 424, 439 Similar modulo k, 260 Simple system of numbers,
455, 458 Solution  of alg.   equations,
407-8
Sous-double, 33 Squares, 52, 54, 284-6, 358,
361, 366, 453-464 Stencil, 349, 356, 359 Substitutions, 75, 78-80, 82,
85, 158, 232, 262 Sum of divisors, 5,  18, 19,
22, 42, 48, 52-8, 135, 139,
279-325, 445, 450 ------------------/cth powers of
divisors, 38, 123, 151, 286-
325, 450 -------------------------integers
<n, 95, 106, 121,123, 126,
140, 332
------------four squares, 283
------------------two squares,
247, 286, 340, 360, 381-2,
390, 402-3 Superfluos, 3, 4 Symbolic, 99,119,124,141-2,
144-5, 148, 248, 250, 278,
296, 395, 399, 402, 449
Symbols, E(n\ 281; Er(n), 296; F(a, N), 84; Fr, 375; H(m), Hm, 264; Jk(n), 147; Mq, 31; fJL(n)} 441; 0, 305; Pm, 33; <£(n), 61, 113; <frfc(rc), 140; qu> 105, 109; «*(n), 48; \$„, 95; tfn.ni, 96; <r(n), 53, 279, 446; <rk(n),
0(n),429; Un, un, 393; r(«), 292; [x], 115, 276; /w, 42; *before author, not available.
Symmetric functions mod. p, 70, 95, 106, 143
-   number,   112,   455, 463-4
Tables, 10, 14, 16, 18, 21-2, 25, 27, 30-2, 37-8, 45, 48-9, 54-5, 110-2, 126, 135, 137, 140, 156-7, 160-79, 181, 183, 185. 187-203, 213, 217, 219, 222, 244-5, 248-51, 254, 262, 296, 308, 318, 331, 339-41, 347-58, 361-4, 366-7, 379, 381-4, 386, 388, 390-1, 399, 417, 422, 432, 446, 457
Talmud, 337
Totient, 124-5, 148, 153, 246
- point, 154 Totitives, 98, 124, 130-1, 246
- all primes, 132, 134 Triangular number, 7, 9, 20,
59, 284, 290, 295, 302, 310, 373, 425, 427 Trinomials, factors of, 391
tlberflussig, 3 tfoerschiessende, 3 Ubervollstandig, 3 Unvollkommen, 3 Unvollstandig, 3
Verwandte, 38, 47 Vollkommen, 3 Vollstandig, 3
Wilson's theorem, 59-91, 99, 103, 275
-, converse   of,
63, 427-8
-, generalization
of, 65, 68-74, 77-84, 87, 90-1 (see Galois)
Zeta function, 121, 125-7, 134,139,149,292-3,298-9, 310,318,322,324,328,331, 439, 448```